The University of Wyoming King Air aircraft was the primary instrument platform for turbulence measurements in the bottom half of the convective boundary layer during 15 July-13 August 1996. A total of 12 successful research flights were made, each of about 4.5-h duration. Crosswind (east-west) flight patterns were flown in Oklahoma and Kansas over three sites of different land use: forest, pasture, and crops.Measurements of mean values, turbulent deviations, and turbulent fluxes of temperature, moisture, and momentum were made to test theories of convective transport, the radix layer, and cumulus potential. Additional portions of each flight included slant soundings and near-surface horizontal flights in order to determine mixed layer (ML) scaling variables such as ML depth z., Deardorff velocity and buoyancy velocity wR. While the ML was shallower and the ground wetter than anticipated based on climatology, a high-quality dataset was obtained.

In the middle of the convective atmospheric boundary layer is often a deep layer of vertically uniform wind speed (M UL), wind direction, and potential temperature (UL). A radix layer is identified as the whole region below this uniform layer, which includes the classic surface layer as a shallower subdomain. An empirical wind speed (M) equation with an apparently universal shape exponent (A) is shown to cause observations from the 1973 Minnesota field experiment to collapse into a single similarity profile, with a correlation coefficient of roughly 0.99. This relationship is M/M UL ϭ F(z/z R), where F is the profile function, z is height above ground, and z R is depth of the radix layer. The profile function is F ϭ (z/z R) A exp[A(1 Ϫ z/z R)] in the radix layer (z/z R Յ 1), and F ϭ 1 in the uniform layer (z R Ͻ z Ͻ 0.7z i). The radix-layer equations might be of value for calculation of wind power generation, wind loading on buildings and bridges, and air pollutant transport. The same similarity function F with a different radix-layer depth and shape exponent is shown to describe the potential temperature () profile: (Ϫ UL)/(0 Ϫ UL) ϭ 1 Ϫ F(z/z R), where 0 is the potential temperature of the air near the surface. These profile equations are applicable from 1 m above ground level to the midmixed layer and include the little-studied region above the surface layer but below the uniform layer. It is recommended that similarity profiles be formulated as mean wind or potential temperature versus height, rather than as shears or gradients versus height because shear expressions disguise errors that are revealed when the shear is integrated to get the speed profile. G. This layer is above the boundary layer. Next is the entrainment zone, a region of subadiabatic temperature profiles, overshooting thermals, intermittent turbulence, and wind shear (Deardorff et al. 1980). Further down is a region where wind speed and direction are nearly uniform with height, z. This is the uniform layer (UL), where the wind speed is M UL and the potential temperature is UL. The wind is subgeostrophic because thermals communicate surface drag information via nonlocal transport. Traditionally, the term ''mixed layer'' is reserved for the whole turbulent region between the surface and the average ML top, z i ; hence,

In the middle of the convective boundary layer, also known as the mixed layer, is a relatively thick region where wind speed and potential temperature are nearly uniform with height. Below this uniform layer (UL), wind speed decreases to zero at the ground, and potential temperature increases to the surface skin value. This whole region below the UL is called the radix layer (RxL), and is of order hundreds of meters thick. Within the bottom of the RxL lies the classical surface layer (order of tens of meters thick) that obeys traditional Monin-Obukhov similarity theory.The RxL depth is shown to depend on friction velocity, Deardorff velocity, and boundary layer depth. The wind RxL is usually thicker than the temperature RxL. Using RxL depth, UL wind speed, and UL potential temperature as length, velocity, and temperature scales, respectively, one can form dimensionless heights, velocities, and temperatures. When observations obtained within the RxL are plotted in this dimensionless framework, the data collapse into similarity curves. This data collapse is tightly packed for data collected over singlelocation homogeneous surfaces, and shows more scatter for data collected along 72-km flight tracks over heterogeneous surfaces. Empirical profile equations are proposed to describe this RxL similarity. When these profile equations are combined with the flux equations from convective transport theory, the results are new flux-profile equations for a deep region within the bottom of the convective boundary layer.These RxL profile similarity equations are calibrated using data from four sites with different roughnesses: Minnesota, BLX96-Lamont, BLX96-Meeker, and BLX96-Winfield. The empirical parameters are found to be invariant from site to site, except for the profile shape parameter for wind speed. This parameter is found to depend on standard deviation of terrain elevation, rather than on the aerodynamic roughness length. The resulting parameter values are compared with independent data from a forested fifth site, Koorin, and it is found that displacement height must be subtracted from all the heights in the RxL profile equations. The resulting profile equations could be useful for calculating wind loading on bridges, wind turbine power estimation, air pollutant transport, or other applications where wind speeds or temperatures are needed over the bottom hundreds of meters of the convective boundary layer.

A virtual research aircraft was flown through a synthetic atmospheric boundary layer to help design a real flight plan that would allow robust turbulence statistics to be obtained in a heterogeneous, evolving, convective boundary layer. The synthetic boundary layer data consisted of a field of coherent, large-diameter, thermal updraft/downdraft structures, superimposed in random smaller-scale turbulence having a Gaussian distribution. These large and small eddy perturbations, with scales set from published empirical relationships, were superimposed on the expected mean profiles of wind and potential temperature. The goal was to determine whether sufficiently robust line-averaged statistics could be gathered to study a new similarity theory for the radix layer, the bottom fifth of the convective boundary layer, where mean profiles are not uniform with height. After testing a variety of flight patterns with the synthetic data, a vertical zigzag pattern of slant ascent/descent legs was selected as the best compromise, given typical aircraft flight and safety constraints. This flight pattern was then successfully flown with the University of Wyoming King Air aircraft in the real atmosphere during Boundary Layer Experiment 1996 (BLX96) over Oklahoma and Kansas. Postexperiment comparison revealed that the synthetic data exhibited less scatter than the actual data, perhaps caused by a heterogeneous surface and a nonstationary boundary layer. Based on this comparison, some practical recommendations are given for future use of synthetic boundary layer data.

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